Problem: Determine the intercepts of the line. $-4x+7=2y-3$ $y$ -intercept: $\Big($
The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}-4\cdot0+7&=2y-3\\ 7&=2y-3\\ 10&=2y\\ 5&=y\end{aligned}$ So the $y$ -intercept is $\left(0,5\right)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}-4x+7&=2\cdot{0}-3\\ -4x+7&=-3\\ -4x&=-10\\ x&=2.5\end{aligned}$ So the $x$ -intercept is $\left(2.5,0\right)$. In conclusion, The $y$ -intercept is $\left(0,5\right)$. The $x$ -intercept is $\left(2.5,0\right)$.